MAT 402 -- Topics in Number Theory (Spring 2014)
Time and Place : TuTh 10-11:20 pm; Library N4000
Instructor : Radu Laza
Office : Math Tower 4-121
Email : rlaza@math.sunysb.edu
Office Hours: TuThr 11:30-12:30 (my office), by appointment, Thr 1-2 in P143 (advising)
Overview
This is a research seminar for undergraduates in mathematics. The broad topic of the class is "Number Theory" (especially computational aspects and Cryptography). The goal of this class is to expose you to more advanced topics in math, things that you will not typically encounter in the usual undergraduate courses.
For the first half of the semester we will follow:
W. Stein, Elementary Number Theory (Primes, Congruences, and Secrets), freely available online, or you can buy a hardcopy.
I also recommend you to install SAGE, a freely available software package for number theoretic computations.
Schedule
The first half of the semester, we will cover the textbook. Specifically:
- [Jan 28, 30, Feb 6] - Review Abstract Algebra and Basic Arithmetic
- [Feb 11, 18] - Public-key Cryptography
- [Feb 20, 25] - Quadratic Reciprocity
- [Feb 27, Mar 4] - Continued Fractions
- [Mar 6, 11, 13] - Elliptic Curves
At this point, we should have enough background to go into more advanced subjects. After Spring Break, we will discuss a number of specialized topics depending on your interests.
- [Mar 25, 27] - Topics assignment / Computational examples using SAGE
- Student presentations
- [4/3] A.R. - Distribution of prime numbers (Note the related colloquium by Y. Zhang)
- [4/10] J.O. - Good Codes/Bad Codes
- [4/24] S.A. - Continued Fractions
- [4/24] N.E. - Fractals
- [5/1] M.M. - Quadratic Reciprocity
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